MinT - Information on Result #1020560

Information on Result #1020560

Linear OOA(2¹⁷⁴, 78, F₂, 3, 56) (dual of [(78, 3), 60, 57]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁷⁰, 39, F₂, 3, 28) (dual of [(39, 3), 47, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁷⁰, 42, F₂, 3, 28) (dual of [(42, 3), 56, 29]-NRT-code), using
  - extracting embedded OOA [i] based on digital (42, 70, 42)-net over F₂, using
    - trace code for nets [i] based on digital (7, 35, 21)-net over F₄, using
      - net from sequence [i] based on digital (7, 20)-sequence over F₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
        an explicitly constructive algebraic function field [i]
linear OOA(2¹⁰⁴, 39, F₂, 3, 56) (dual of [(39, 3), 13, 57]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁰⁴, 42, F₂, 3, 56) (dual of [(42, 3), 22, 57]-NRT-code), using
  - strength reduction [i] based on linear OOA(2¹⁰⁴, 42, F₂, 3, 57) (dual of [(42, 3), 22, 58]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OOA(4³¹, 14, F₄, 3, 28) (dual of [(14, 3), 11, 29]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,13P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
      2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.